Questions: 2/9 x - 4 = 2/3

2/9 x - 4 = 2/3
Transcript text: 27.) $\frac{2}{9} x-4=\frac{2}{3}$
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Solution

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Solution Steps

To solve the equation \(\frac{2}{9} x - 4 = \frac{2}{3}\), we need to isolate the variable \(x\). First, add 4 to both sides of the equation to eliminate the constant term on the left side. Then, multiply both sides by the reciprocal of \(\frac{2}{9}\) to solve for \(x\).

Step 1: Isolate the Variable Term

To solve the equation \(\frac{2}{9}x - 4 = \frac{2}{3}\), we first isolate the term containing \(x\) by adding 4 to both sides of the equation:

\[ \frac{2}{9}x - 4 + 4 = \frac{2}{3} + 4 \]

This simplifies to:

\[ \frac{2}{9}x = \frac{2}{3} + 4 \]

Step 2: Simplify the Right Side

Next, we simplify the right side of the equation:

\[ \frac{2}{3} + 4 = \frac{2}{3} + \frac{12}{3} = \frac{14}{3} \]

So the equation becomes:

\[ \frac{2}{9}x = \frac{14}{3} \]

Step 3: Solve for \(x\)

To solve for \(x\), multiply both sides by the reciprocal of \(\frac{2}{9}\), which is \(\frac{9}{2}\):

\[ x = \frac{14}{3} \times \frac{9}{2} \]

Simplifying the right side:

\[ x = \frac{14 \times 9}{3 \times 2} = \frac{126}{6} = 21 \]

Final Answer

\(\boxed{x = 21}\)

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